The following information shows the result of the orbit fit based on Gary Bernstein's method. Most of the information should be self-explanatory. Take special note that while the original Bernstein software works with barycentric coordinates, we convert these results into a heliocentric coordinate system.
# Object: 13RQ157 # Created Fri Apr 19 01:14:57 2024 # Orbit generated by ELGB # -->Covariance matrix from a Bernstein fit # Fitting 12 observations of 12 # Arc: 8.81y # First observation: 2013/09/11 # Last observation: 2022/07/04 # Chi-squared of fit: 2.00 DOF: 18 RMS: 0.07 # Min/Max residuals: -0.10 0.15 # Exact a, adot, b, bdot, g, gdot: 1.651127E-05 2.862213E-02 2.423744E-06 4.353821E-03 2.802251E-02 -2.450316E-03 # Covariance matrix: 3.1189E-13 -6.1061E-14 7.3653E-15 2.1930E-15 3.0611E-13 3.8909E-14 -6.1061E-14 2.1466E-13 -1.1118E-14 4.1385E-14 7.9115E-13 1.0428E-12 7.3653E-15 -1.1118E-14 2.3143E-13 -3.8259E-14 -1.2625E-14 -4.4574E-14 2.1930E-15 4.1385E-14 -3.8259E-14 2.1177E-14 1.9845E-13 2.2815E-13 3.0611E-13 7.9115E-13 -1.2625E-14 1.9845E-13 5.1449E-12 4.9167E-12 3.8909E-14 1.0428E-12 -4.4574E-14 2.2815E-13 4.9167E-12 5.7145E-12 # lat0 lon0 xBary yBary zBary JD0 13.407652 -40.287638 -0.481585 0.205295 -0.860852 2456546.664558 # Heliocentric elements and errors Epoch: 2456546.5000 = 2013/09/11 Mean Anomaly: 268.21116 +/- 0.218 Argument of Peri: 157.84185 +/- 0.177 Long of Asc Node: 263.83265 +/- 0.001 Inclination: 15.54850 +/- 0.000 Eccentricity: 0.07400858 +/- 0.0001 Semi-Major Axis: 36.26766372 +/- 0.0111 Time of Perihelion: 2476887.1660 +/- 55.5 Perihelion: 33.58354560 +/- 0.0105 Aphelion: 38.95178184 +/- 0.0121 Period (y) 218.4176 +/- 0.10 # Ecliptic coordinates at JD0 (AU and AU/d) Ecliptic X 27.46589137 +/- 0.0021 Ecliptic Y -22.64826286 +/- 0.0018 Ecliptic Z 8.27477343 +/- 0.0007 Ecliptic XDOT 0.00154919 +/- 0.0000 Ecliptic YDOT 0.00234634 +/- 0.0000 Ecliptic ZDOT 0.00035841 +/- 0.0000 # Distances at JD0 (AU) Heliocenter to KBO 36.54851578 +/- 0.0020 Geocenter to KBO 35.68569321 +/- 0.0029 # Hcoef: 7.78
The following table shows the complete astrometric record for 13RQ157. The first three columns show the date of observation. The next six columns are RA and DEC. The next column (when provided) is the observed magnitude and filter. The next column is the object name (13RQ157) followed by the observatory code and reference code for the source of the astrometry.
2013 09 11.16378 21 11 47.548 -02 08 48.21 23.7r 13RQ157 W84 C~52RP 2013 09 11.16515 21 11 47.552 -02 08 48.11 23.3i 13RQ157 W84 C~52RP 2013 09 13.11509 21 11 39.375 -02 09 46.15 22.9i 13RQ157 W84 C~52RP 2013 09 13.11648 21 11 39.358 -02 09 45.96 22.9z 13RQ157 W84 C~52RP 2013 10 11.04758 21 10 13.727 -02 23 12.67 22.9z 13RQ157 W84 C~52RP 2016 09 08.06550 21 29 55.724 +00 06 09.44 23.1i 13RQ157 W84 C~52RP 2016 09 26.05493 21 28 41.472 -00 03 25.38 23.5r 13RQ157 W84 C~52RP 2016 09 26.05631 21 28 41.475 -00 03 25.43 23.1i 13RQ157 W84 C~52RP 2017 10 11.00640 21 33 57.176 +00 33 27.31 23.4i 13RQ157 W84 C~52RP 2017 10 22.03122 21 33 36.478 +00 28 01.11 23.3i 13RQ157 W84 C~52RP 2022 07 04.367650 22 11 51.417 +04 56 20.72 23.4G 13RQ157 G37 C~5i2s 2022 07 04.432770 22 11 51.215 +04 56 21.18 13RQ157 G37 C~5i2s
The following table shows the residuals to the orbit fit. The first coumn is the point number. The second column is the time, in years, measured from the first observation. The third and fifth columns are the regularized positions used in the orbit fit. The fourth and sixth columns are the residuals, in arc seconds, for RA and Dec respectively.
1 0.0000 0.00 -0.07 0.00 -0.02
2 0.0000 0.00 0.08 0.00 0.12
3 0.0053 0.00 0.07 0.00 -0.08
4 0.0053 0.00 -0.10 0.00 0.15
5 0.0818 0.00 0.02 0.00 -0.04
6 2.9922 0.00 0.07 0.00 0.00
7 3.0415 0.00 -0.09 0.00 -0.08
8 3.0415 0.00 0.03 0.00 -0.09
9 4.0817 0.00 0.09 0.00 0.03
10 4.1119 0.00 -0.01 0.00 -0.05
11 8.8110 0.00 -0.05 0.00 -0.01
12 8.8111 0.00 -0.01 0.00 0.07
The following table comes from a 10My integration of the orbit of the object. Three columns are shown. The first column is the result of integrating the nominal orbit. The other two columns are based on clones of the nominal orbit that are +/- 3 sigma from the nominal orbit. If all three types agree then the classificiation is deemed secure. The basis for these calculations is described in more detail in AJ, 129, 1117 (2005). Any use made of these calculations should refer to and credit this publication and the Deep Ecliptic Survey Team.
13RQ157 quality flag:3 Type: 4:3E 4:3E 4:3E axisobj 36.369 36.369 36.369 ecceobj 0.075 0.075 0.075 incobj 15.562 15.562 15.562 qmin 32.961 32.880 32.961 qmax 40.357 40.517 40.375 amean 36.479 36.479 36.479 amin 36.064 36.090 36.094 amax 36.886 36.894 36.888 emean 0.073 0.075 0.074 emin 0.038 0.042 0.042 emax 0.095 0.100 0.097 imean 18.590 18.706 18.599 imin 15.019 16.265 15.511 imax 20.590 20.575 20.543 excite_mean 0.327 0.330 0.328 fracstop 1.000 1.000 1.000 cjmean 2.904 2.903 2.904 libcent 0 177.9 177.4 179.7 libamp 0 131.7 127.5 125.5 libcent 1 -180.0 -180.0 -180.0 libamp 1 -180.0 -180.0 -180.0 libcent 2 -180.0 -180.0 -180.0 libamp 2 -180.0 -180.0 -180.0 libcent 3 -180.0 -180.0 -180.0 libamp 3 -180.0 -180.0 -180.0 libcent 4 -180.0 -180.0 -180.0 libamp 4 -180.0 -180.0 -180.0 kozaimean 179.8 179.4 179.2 kozaiamp 180.0 180.0 180.0